I’ve recently found out an odd thing. It seems that calculating Collatz sequence lengths with no caching at all is over 2 times faster than using std::unordered_map
to cache all elements.
Note I did take hints from question Is gcc std::unordered_map implementation slow? If so - why? and I tried to used that knowledge to make std::unordered_map
perform as well as I could (I used g++ 4.6, it did perform better than recent versions of g++, and I tried to specify a sound initial bucket count, I made it exactly equal to the maximum number of elements the map must hold).
In comparision, using std::vector
to cache a few elements was almost 17 times faster than no caching at all and almost 40 times faster than using std::unordered_map
.
The problematic benchmark is:
#include <iostream>
#include <unordered_map>
#include <cstdint>
#include <ctime>
std::uint_fast16_t getCollatzLength(std::uint_fast64_t val) {
static std::unordered_map <std::uint_fast64_t, std::uint_fast16_t> cache (1, 2168611);
if(cache.count(val) == 0) {
if(val%2 == 0)
cache[val] = getCollatzLength(val/2) + 1;
else
cache[val] = getCollatzLength(3*val+1) + 1;
}
return cache[val];
}
int main()
{
std::clock_t tStart = std::clock();
std::uint_fast16_t largest = 0;
for(int i = 1; i <= 999999; ++i) {
auto cmax = getCollatzLength(i);
if(cmax > largest)
largest = cmax;
}
std::cout << largest << '\n';
std::cout << "Time taken: " << (double)(std::clock() - tStart)/CLOCKS_PER_SEC << '\n';
}
It outputs: Time taken: 0.761717
Whereas a benchmark with no caching at all:
#include <iostream>
#include <unordered_map>
#include <cstdint>
#include <ctime>
std::uint_fast16_t getCollatzLength(std::uint_fast64_t val) {
std::uint_fast16_t length = 1;
while(val != 1) {
if(val%2 == 0)
val /= 2;
else
val = 3*val + 1;
++length;
}
return length;
}
int main()
{
std::clock_t tStart = std::clock();
std::uint_fast16_t largest = 0;
for(int i = 1; i <= 999999; ++i) {
auto cmax = getCollatzLength(i);
if(cmax > largest)
largest = cmax;
}
std::cout << largest << '\n';
std::cout << "Time taken: " << (double)(std::clock() - tStart)/CLOCKS_PER_SEC << '\n';
}
Outputs Time taken: 0.324586
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